When I check software update for my watch it tells me:"watch OS 3.1.3Your software is up to date"

There's no option to go to 3.2

Ok, let me answer my own question: After updating my phone to 10.3,
the Watch App now shows WatchOS 3.2 to be available. It might be a
coincidence, but I suspect that 10.3 on the phone is a pre-requisite for
3.2 on the watch